Answer
a) True
b) False
c) True
d) False
e) True
f) False
g) True
h) False
i) False
j) True
Work Step by Step
a) all real numbers can be squared and will give a real number.
b) counter-example: x=-1. No real number y squared can equal -1.
c) All number multiplied by 0 equal 0
d) addition is always commutative for real numbers
e) for any != 0, we can take a number y=1/x which multiplied by x will always equal 1 for real numbers
f) Only one y will satisfy the condition for each x.
g) No matter the x chosen, we can use a y = 1-x. Which means that for each x, at least one y satisfy x+y=1.
h) we can do a proof for this:
2x+4y = 5 <=> 2(2 - 2y) + 4y = 5
4 - 4y + 4y = 5
4 = 5 . which is false.
i) Counter-Example: let's take x = 2. It means that y = 0. For the conditions to be satisfied, 2x - y = 4-0 = 4 and not 1 as indicated in the statement.
j) No matter x or y chosen, we can always add them and divide them by two to give a real number z. S
